-quasiconvexity: weak-star convergence and the gap

Irene Fonseca, Stefan Müller, and Giovanni Leoni

Contact the author: Please use for correspondence this email.
Submission date: 11. Feb. 2003
Pages: 35
published in: Annales de l'Institut Henri Poincaré / C, 21 (2004) 2, p. 209-236 
DOI number (of the published article): 10.1016/j.anihpc.2003.01.003
Bibtex
MSC-Numbers: 35E99, 49J45, 74B20
Keywords and phrases: a-quasiconvexity, gap, non-standard growth conditions, lower semicontinuity, sobolev embedding theorem, radon-nikodym decomposition theorem
Download full preprint: PDF (337 kB), PS ziped (281 kB)

Abstract:
Lower semicontinuity results with respect to weak- convergence in the sense of measures and with respect to weak convergence in are obtained for functionals

where admissible sequences satisfy a first order system of PDEs . We suppose that has constant rank, f is -quasiconvex and satisfies the non standard growth conditions

with for , for p>N-1. In particular, our results generalize earlier work where reduced to for some .